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bility be equal to half certainty, it is called doubtful; and if the pro- 

 bability be Icfs than half certainty it is faid to be improbable. 



Since the chances for happening or failing are equal to the 

 whole numbfer of chances, the probabilities of the happening and 

 failing of the event are together = i, that is, equal to certainty. 



Therefore the probability of happening is equal to" the diffe- 

 rence between certainty and the probability of failing; and the 

 probabity of failing equal to the difference between certainty and I 



the probability of happening. 



From what has been faid it follows, that the probability that 

 a witnefs tells truth, in a given inflance, will be expreffed by a 

 fradion whofe numerator is the number of chances for his telling . 

 truth, and the denominator the fum of the number of chances for 

 his telling truth, and for his telling falfliood together. 



In like manner, the probability that an argument is true, is to 

 be eflimated by the' ratio of the number of chances for its truth 

 to the number of chances for its truth and falfhood together. 



It is true, that in neither of thefe latter cafes can we, in 

 general, determine the actual number of charices j neverthx^lefs in 

 all tafcs where a perfon perceives the probability of an event, 

 he mufl at the fame time perceive, that there muft be fomc finite, 



determinate 



